Question

Consider the following information on Stocks I and II:

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Stock I	Stock II
Recession	.21	.040	−.36
Normal	.61	.350	.28
Irrational exuberance	.18	.210	.46

The market risk premium is 11.6 percent, and the risk-free rate is 4.6 percent.
a.	Calculate the beta and standard deviation of Stock I. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers to 2 decimal places, e.g., 32.16.)
b.	Calculate the beta and standard deviation of Stock II. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers to 2 decimal places, e.g., 32.16.)
c.	Which stock has the most systematic risk?
d.	Which one has the most unsystematic risk?
e.	Which stock is “riskier”?

	a. Beta _____ Standard deviation ____% b. Beta _____ Standard deviation _____% c. Most systematic risk _____ d. Most unsystematic risk _____ e. "Riskier" stock_______

Answer 1

In order to calculate beta and standard deviation of stock, let us first calculate expected return of stock

Expected return of stock I = (0.21*0.04) + (0.61*0.35) + (0.18*0.21) = 0.2597

Expected return of stock II= (0.21*-0.36) + (0.61*0.28) + (0.18*0.46) = 0.178

a)

For stock I

Standard Deviation of stock

= [0.21 × (0.04-0.2597)² + 0.61 × (0.35-0.2597)² + 0.18 × (0.21-0.2597)²]^1/2

= [0.0101362989 + 0.0049739949 + 0.0004446162]^0.5

= 0.01555491^0.5 = 0.12471932488592 = 0.12

Beta

Expected return = risk free rate + (Beta of stock * market risk premium)

0.2597 = 0.046 + Beta *0.116

0.2137 = Beta *0.116

Beta = 0.2137 /0.116

Beta = 1.8422 = 1.84

b)

For stock II

Standard Deviation of stock

= [0.21 × (-0.36-0.178)² + 0.61 × (0.28-0.178)² + 0.18 × (0.46-0.178)²]^1/2

= [0.06078324 + 0.00634644 + 0.01431432 ]^0.5

= 0.081444^0.5 = 0.28538395189 = 0.29

Beta

Expected return = risk free rate + (Beta of stock * market risk premium)

0.178 = 0.046 + Beta *0.116

0.132 = Beta *0.116

Beta = 0.132 /0.116

Beta = 1.13793 = 1.14

c)

Beta determines the systematic risk of the stock.

For stock I

So to measure the systematic risk = beta of stock/ market risk = 1.84/ 0.116 = 15.86

For stock II

So to measure the systematic risk = beta of stock/ market risk = 1.14/ 0.116 = 9.83

Stock I has higher systematic risk when compared to Stock II

d)

Unsystematic risk = Variance – systematic risk

Variance = square of standard deviation

Systematic risk = beta

For stock I

Unsystematic risk = 0.01555491 – 1.84 = -1.82444509

For stock II

Unsystematic risk = 0.081444– 1.14 = -1.058556

So, the unsystematic risk for both stocks is negative. Considering negative sign, the unsystematic risk for stock II is higher.